Ryan McDonagh scored in the first period for New York, which has won seven of eight overall and five in a row at home.
"I think going into this game we felt like this a good test coming at the right time for us," said Lundqvist who earned his 401st career win. "You can feel that we're getting closer here and this is just another opportunity for us to work on our game against a really good team."
Alex Ovechkin scored a second-period power-play goal for Washington. Ovechkin's goal was his 22nd against Lundqvist, the most he has scored against any goalie in his career.
The first-place Capitals lost their second straight after a six-game winning streak. Philipp Grubauer made 28 saves for Washington.
Tied 1-1 entering the third period, Grubauer made two saves on Jimmy Vesey. Lundqvist answered as he made a nice glove stop on John Carlson's slap shot about seven minutes into the period.
Zuccarello broke the tie after Mika Zibanejad won a faceoff in the Washington zone and sent a pass to Chris Kreider. Kreider passed to Zuccarello, who beat Grubauer for his 12th of the season at 8:37. The goal was Zuccarello's first of his career against Washington in the regular season.
The Capitals controlled the play in the second period, outshooting New York 11-4. Lundqvist made a key save on Brett Connolly. Justin Williams broke his stick on a tap-in attempt and Daniel Winnik hit the post.
"In this league with the fine line that separates every team, you have to find different ways, and that's what we did," Rangers coach Alain Vigneault said. "We went in there in the third more on our toes. We had to check real well and we had to get some saves, and we did. That's a real strong hockey team. They're not in first place in the league for nothing."
With Washington on the power play late in the second period, Lundqvist stopped Ovechkin's backhand. However, the Capitals' star tied the game 1-1 as he took a cross-ice pass from Lars Eller and beat Lundqvist with a wrist shot that was deflected by defenseman Nick Holden at 17:24 for Ovechkin's 27th goal of the season.
Both teams were coming off losses that ended six-game winning streaks. Washington lost in a shootout in Detroit on Saturday and the Rangers lost to the Islanders on Thursday.
Despite the matinee start, the Rangers got off to a fast start. New York outshot Washington 19-10 and forced Grubauer to make several outstanding saves. The backup goalie stopped Kevin Hayes twice in close, made a save on Kreider's breakaway attempt and he stopped Oscar Lindberg in the final minute.
"We were atrocious in the first," Capitals coach Barry Trotz said. "We played poorly and Gruby was outstanding. It could have been 5-0.
"In the second and third we had the better chances and the majority of the play. I felt we managed the game much better. They had 11 shots in the last two periods, but they found a way to win."
The Rangers opened the scoring on Ryan McDonagh's third goal of the season . McDonagh skated into the zone and put a shot on net. Then the Rangers captain skated toward the net and wristed the rebound past Grubauer at 7:49 of the first period.
"We were just moving too slow," Capitals defenseman Matt Niskanen said of his team's first period. "Moving the puck too slow, and not moving our legs quick enough, and it showed."
Zibanejad nearly made it 2-0 on a power-play goal late in the period. The goal was disallowed after a review for offside.
Notes: The Rangers announced on Saturday that they will raise the banner of Jean Ratelle's No. 19 to the rafters next season. He played parts of 16 seasons with the Rangers from 1960-61 to 1975-76. He had 336 goals, 481 assists for 817 points in 862 games. He was inducted into the Hockey Hall Fame in 1985 and was recently selected as one of the NHL's top 100 players. The Rangers lead the NHL in third-period goals this season with 81. Vigneault earned his 182nd win as Rangers coach, passing Frank Boucher for sole possession of third place on the franchise's wins list among head coaches. The only head coaches who have earned more wins with the Rangers are Emile Francis and Lester Patrick.